A quadratic equation can be solved using the discriminant. The roots of the quadratic equation: x1=2aD−b x2=2a−D−b where D = b^2 - 4*a*c - it is the discriminant. Because a=1 b=−1 c=−90 , then
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (1) * (-90) = 361
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or x1=10 x2=−9
Vieta's Theorem
it is reduced quadratic equation px+q+x2=0 where p=ab p=−1 q=ac q=−90 Vieta Formulas x1+x2=−p x1x2=q x1+x2=1 x1x2=−90